1 DFS Studies on the Main Linac with Rnd-walk-like motion LET Beam Dynamics Workshop 12 th December 2007 Freddy Poirier

2 Dynamic Impact of Global Correction Pac07 paper (Eurotev- report ): –On tolerances Shown: results of ATL ground motion after time T Within this model, the girders (support of cryomod.) are vertically moved. A was chosen to be 4×10-18 m.s-1. At every point a perfect one-to-one steering correction was applied to the model and the BPM resolution was set to a perfect resolution (0 mm). The linac is straight and wakefields are included. Global correction  increase the long-term stability of the emittance with diffusive ground motion Correction throughout this study: Energy correlation numerically removed

3 DFS after ATL Start with a misaligned linac –Std errors on elements –100 Rnd Seeds Apply DFS (DMS**) –Weight fixed –Energy modification strategy: -20% gradient -20% initial beam –Segmentation (40 quad, 20 overlap) –Final ( energy corrected*) mean Emittance = ~22 nm Apply random walk (ATL) A=4 10^-18 m/s Then apply DMS algorythm –Found that the time scale over which the DMS was applied do give good results: DMS works. (energy correlation removed). This is probably because the additional errors are small compared to the initial uncorrelated random errors: –Betatron wavelength sets the scale  ~ 200m: –  2 ~ (4  )  10 6  200   ~ 28  m *Correction throughout this study: Energy correlation numerically removed **DMS: Dispersion Matched Steering (as dealing with a curved beamline) Emittance value stable over studied time scale.

4 Rnd-walk-like correlation Apply random misalignment with a random-walk-like correlation, where the variance of the differential offset between two adjacent points is proportional to the distance between them:  2 = C L –In order to achieve a total of a ~1cm RMS offset at the end of the linac, we have C = 1 cm 2 / 10 km ~ m Strategy is as follow: –Misaligned elements (std errors) –Apply rnd walk –Apply DMS Check out the final emittance at the end of linac. RMS= 7.6 mm at end of linac C= 6 10^-9 m. Offset at the end of linac (100 seeds):

5 Mean Vertical Emittance (100 seeds) Curved machine, with wakefields. Misalignment errors has been applied prior to this study Apply CL model Apply DMS Fixed weight Wdiff=40 ~7 mm offset *From M.Schloesser (DESY)  0.5mm/km + 2mm (1 st primary ref pt: C=4.2 10^-9) *From C.Adolphsen (wiki)  2mm/km global (but old value), C= 4 10^-9m *From RDR (ML p.234, 1sigma tolerance)  200 um/200m, C= 2 10^-10m *From ILC/GDE meeting at DESY  200 um / 600m, C= ^-11 m Present discussion between the metrology people and the physics accelerator group. Rnd-walk-like Result (1 mm)

6 Impact of Wakes Tesla wakefield in use here. C=3.10^-8 m (High value) Mean corrected Emittance w/wo wakes: The main reason of the emittance increase is coming from the wakefield (note: cavities are moved away of the curved beamline)

7 Weight Effect –In previous studies W_diff=40 –Used in benchmarking, –Found to be in a stable region to minimize the final emittance. BPM resolution=5um (no scale error) DMS optimisation depends on constrains: Region of stability of W_diff is reduced

8 Weight Effect (2) Choice of 2 different weight: –Wdiff = 40 –Wdiff = um/600m A smaller weight here helps to keep the emittance growth lower wrt to C. 200 um/600m

9 Conclusion –With the simple CL model, 200um/600m no significant impact on the corrected emittance. –Though the impact of a random-walk-like correlation could be non negligible if alignment was worse. The results are highly dependent on the values of the alignments (need to be precise on what we mean) –Here the choice of a wrong weight for the DMS could make things worse (scanning the weight would resolve the problem). More work (refinement): –Rnd-walk-like CL model too simple? –Binning effect? Iterations?

10 Additional slides

11 Eyc_mini (no CL model) =22.2 nm at W=20 Eyc_mini (C=610^-9m) = 26.2 nm at W=5 Projected Emittance Emittance with energy correlation numerically removed Ey_mini (no CL model) =25.0 nm at W=20 Ey_mini (C=610^-9m) = 37.9 nm at W=10

12 Offset along the linac